Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+6y &= -4 \\ -2x+2y &= -3\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = -2y-3$ Divide both sides by $-2$ to isolate $x$ $x = {y + \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $-5({y + \dfrac{3}{2}}) + 6y = -4$ $-5y - \dfrac{15}{2} + 6y = -4$ Simplify by combining terms, then solve for $y$ $1y - \dfrac{15}{2} = -4$ $1y = \dfrac{7}{2}$ $y = \dfrac{7}{2}$ Substitute $\dfrac{7}{2}$ for $y$ in the top equation. $-5x+6( \dfrac{7}{2}) = -4$ $-5x+21 = -4$ $-5x = -25$ $x = 5$ The solution is $\enspace x = 5, \enspace y = \dfrac{7}{2}$.